Joint probability density function

Discussion in 'Math' started by boks, Jan 10, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    Let X, Y, and Z have the joint probability density function

    f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2

    find k

    \int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz

    This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...
    Last edited: Jan 10, 2009
  2. steveb

    Senior Member

    Jul 3, 2008
    That looks correct assuming that the joint probability function is zero everywhere else. You didn't say that explicitly, but it seems implied.

    You should have no trouble evaluating that integral.